Decays and decline of Persian and Byzantine Empire.
By the time, conquests by Umar were completed Persian empire ceased to exist. Byzantine on the other hand was driven to its Europe lands where it ruled for few centuries more. But both the empires were crumbling at the time of expansion at least in barren Arab lands. And Persia was wholly desert land and most of it was crippling.
The desert, date palm, and the camel
Desert favored Arabs since they had lived there for centuries. Persia although was largely desert didn’t have warriors that had as much experience as nomadic Arabian tribes. Date-palm was another crucial element that helped Muslims. It is a full-diet dish. Arabs liked it particularly for it is easily portable and packs so much calories in such small package. Byzantine and Persian people were luxury-loving people, who brought large swathes of meals and when ran out of it grew despondent. In addition,
camel was a best friend of Arabs. Camel was naturally an animal made for desert. The enemies came on horses and elephants which grew weary after few days of fighting.
Character of Arabs
The hard life of Jahiliya period had inured Arabs with courage, tenacity, perseverance, and passive endurance, loyalty, and manliness. They possessed all the qualities of warriors and fighters except unity, discipline and respect for order and authority of a nation. Islam and the Caliphate filled these gaps.